text:
Study finds only full 18-hole options for golf course restoration economically viable
News | September 4, 2010
Adam Jensen
ajensen@tahoedailytribune.com
Adam Jensen / Tahoe Daily TribuneProject manager Cindy Walck displays the proposed realignment of holes at Lake Tahoe Golf Course under one of the alternatives for a restoration project at the course during a presentation last week.
SOUTH LAKE TAHOE, Calif. – Dozens of jobs could be at risk under two of the five scenarios being considered for an environmental restoration project at Lake Tahoe Golf Course, according to a recently released economic study.
The feasibility study, which is included in the draft environmental document for the Upper Truckee River Restoration and Golf Course Reconfiguration Project, finds the only economically-viable alternatives are those that retain a full-length, 18-hole golf course.
The environmental document for the project analyzes five alternatives, ranging from leaving the golf course the same to completely removing it.
Alternatives that would shorten the layout of the course to nine holes or an shorter "executive" 18-hole course, move several holes from next to the Upper Truckee River into Washoe Meadows State Park or add additional erosion control measures to the river while keeping the course layout the same are also detailed in the document.
State park officials are expected to choose which option to pursue following the conclusion of the environmental review process.
People who use Washoe Meadows State Park and nearby residents have raised concerns about moving nine holes of the golf course into the state park, while golfers have objected to alternatives that would dramatically change the layout of the course.
The primary goal of the project is to reduce the amount of fine sediment and nutrients entering the lake from the Upper Truckee River. Lake Tahoe's clarity has been in decline for decades because development throughout the Lake Tahoe Basin has allowed more fine sediment and nutrients to enter the lake.
Maintaining $881,000 of annual income to the California State Park system from the golf course is also among the stated goals of the restoration project. The course is in the top five revenue generating areas for the park system and helps pay for the operation of other state parks in the Sierra District.
The course logs more than 22,000 visits and generates about $6.1 million in visitor spending at the South Shore each year, according to the economic feasibility study.
"These revenues would be lost if the golf course closed, and reduced to between approximately $3.5 million and $5.2 million with a reduced-play area (non-traditional length) course," according to the study.
A nine hole or executive length course would result in the loss of 55 jobs between the golf course and other South Shore businesses that benefit from visitor spending, according to the study, which questions whether a nine hole course or short 18 hole course could survive at all.
The feasibility study finds a shorter golf course would be economically unrealistic "under all but the most optimistic of circumstances."
"If the reconfigured golf course can achieve more than 25,000 rounds annually and command green fees above the median rack rate for comparable Tahoe non-traditional length facilities, it may be financially feasible; however, the concessionaire's net revenues would be marginal, making the golf course susceptible to closure," according to the study.
Complete removal or closure of the course would result in the loss of 168 jobs at the South Shore, according to the study. Seventy-six of the jobs would be at the golf course, and 92 jobs would be from other businesses that benefit from visitor spending.
"Earnings by employees generated elsewhere in South Shore by visitors to (Lake Tahoe Golf Course) are estimated to decrease by $287,000 to $880,000 annually with a reduced-play area (non-traditional length) course, and $2 million with no golf course," according to the study.
"The loss in earnings associated with these jobs is approximately $2.7 million, which is money no longer re-circulated within the local economy," the study continues.
Public site tours of the golf course and an open house on the restoration project are scheduled for later this month. The draft environmental document is open for public comment until Nov. 4.
For more information on the project, including how to comment, visit: http://www.restoreuppertruckee.net.


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We offer a whisky sampling package tailored to our guests' individual tastes. We start by discussing your likes and dislikes, talk about the influences on whisky flavour, and suggest three whiskies for you to try. We offer two packages: the Standard package and the Premium, which gives guests a chance to taste a selection of our prime whiskies. and may include a vertical tasting of several whiskys from one distillery. Both packages include three 35cl servings from our collection.
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text:
China: Billionaire gets life term for corruption
May 19, 2012 | Bribery, Politics, Public Service, Uncategorized | 0 |
Lai Changxing
19 May 2012. Lai Changxing became a billionaire by carrying out smuggling activities. He bribed top officials to keep himself out of jail. Former Prime Minister Zhu Rongji once remarked that Lai's crimes were so extreme that executing him three times would not be adequate punishment for him.
Lai, 53, escaped death sentence by fleeing to Canada. He lived there well with his wife and three children for more than a decade. But his brother and his accountant met with unexplained death in prison. Even top Communist Party officials feared that they may be the next to be caught. He paid more than $5 billion in bribes to some 64 government officials and smuggled $4.3 billion worth of luxury cars, cigarettes and petrol.
Canadian government's policy is not to extradite a fugitive if he would face a certain death. Canada agreed to extradite him after obtaining guarantee from the Chinese government that Lai would not be tortured or sentenced to death.
Ottawa court rejected his application for refugee status and the judge called him a "common criminal".
On arrival in China he was convicted of smuggling and offering bribes and sentenced to life in prison.
The Canadian government is pleased with the sentence meted out to him. Foreign Affairs and International Trade spokeswoman Patricia Low-Bedard says China lived up to its assurance that Lai Changxing would not receive the death penalty upon conviction.
Watch this video: Chinese Fugitive Lai Changxing Faces Trial in Xiamen
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NextPalestine: Anti-corruption blogger arrested
Maldives: CPI report puts Maldives among the most corrupt nations.
China: China Securities Regulatory Commission head falls from grace.
Singapore: CNB deputy director takes the stand in Ng Boon Gay's trial
Italy: Berlusconi corruption case

redpajama_set_name: RedPajamaCommonCrawl


The Barack Obama administration has approved the final two permits necessary for Royal Dutch Shell to begin oil drilling in Chukchi Sea off the coast of Arctic Alaska, news reports say.
The Bureau of Safety and Environmental Enforcement (BSEE) has issued "conditional approval" to the last two permits. They grant Shell the go-ahead to drill on the top sections of wells, but not yet deep enough to extract oil, until the company has all safety equipment on-site.
Also, Shell must have emergency equipment to contain a potential blown out well deployable within 24 hours before drilling into the oil zone, the office said.
Earlier, it was discovered that the company's Fennica icebreaker that holds the required equipment, also known as a capping stack, developed a three-feet gash in it.
"Without the required well-control system in place, Shell will not be allowed to drill into oil-bearing zones. As Shell conducts exploratory activities, we will be monitoring their work around the clock to ensure the utmost safety and environmental stewardship," BSEE Director Brian Salemo was quoted by the media as saying.
Fennica has been sent to Oregon for repair. Fixing the gash and returning the vessel to the Arctic may take weeks.
Environmentalists have criticised Shell's drilling plans in the Arctic, which is home to sensitive populations of whales, walrus and polar bears.
The Bureau of Ocean Energy Management of the US Department of the Interior had said earlier that long-term drilling in Chukchi Sea could come with a 75 per cent chance of a major spill in the next 77 years.
For the time being, Shell is planning to drill for data. Its exploratory wells will determine where and how many production wells it could hypothetically drill in the future.


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text:
Assistant Chief Peter Newsham chosen as interim D.C. police chief
August 24, 2016 thewashingtonsun
Assistant D.C. Police Chief Peter Newsham, who frequently is the face of the department as he discusses major crimes before reporters or addresses the D.C. Council, was named interim police chief Tuesday to take over for the retiring Cathy L. Lanier.
Newsham has been an assistant chief for 14 years of his 27 years on the force and now serves as head of the criminal investigation division, overseeing all homicide cases and high-profile robberies, burglaries and assaults.
The 52-year-old, a lawyer and member of the Maryland State Bar Association, will take over Sept. 17, the scheduled last day for Lanier, who is leaving to be chief of security for the National Football League.
Newsham takes on the interim role amid an ongoing search for the next permanent chief under Mayor Muriel E. Bowser (D).
Bowser has said she will concentrate on internal candidates but accept applicants from department outsiders.
In a statement Tuesday, Bowser said that a posting for the chief's opening will be published soon and that after a contender list is winnowed, "a small group of community stakeholders will be involved in vetting final candidates." Sgt. Matthew Mahl, chairman of the police union, said he has been told the labor group will be part of the process.
Bowser hailed Newsham as having "deep roots serving the District" and said he "believes in the power of building relationships with communities as the best way to deter and solve crime. He has served the people of the District of Columbia for almost three decades and in that time has demonstrated his unwavering commitment to the District and to its residents."
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text:
namespace g{namespace Uno{namespace Runtime{namespace Implementation{struct GraphicsContextImpl;}}}}
namespace g{namespace Uno{struct Int2;}}
namespace g{namespace Uno{struct Recti;}}

namespace g{
namespace Uno{
namespace Runtime{
namespace Implementation{

// internal static class GraphicsContextImpl :331
// {
uClassType* GraphicsContextImpl_typeof();
void GraphicsContextImpl__GetBackbufferGLHandle_fn(uGraphicsContext* handle_, uint32_t* __retval);
void GraphicsContextImpl__GetBackbufferOffset_fn(uGraphicsContext* handle, ::g::Uno::Int2* __retval);
void GraphicsContextImpl__GetBackbufferScissor_fn(uGraphicsContext* handle, ::g::Uno::Recti* __retval);
void GraphicsContextImpl__GetBackbufferSize_fn(uGraphicsContext* handle, ::g::Uno::Int2* __retval);
void GraphicsContextImpl__GetInstance_fn(uGraphicsContext* __retval);
void GraphicsContextImpl__GetRealBackbufferHeight_fn(uGraphicsContext* handle, int* __retval);

struct GraphicsContextImpl : uObject
{
    static uint32_t GetBackbufferGLHandle(uGraphicsContext handle_);
    static ::g::Uno::Int2 GetBackbufferOffset(uGraphicsContext handle);
    static ::g::Uno::Recti GetBackbufferScissor(uGraphicsContext handle);
    static ::g::Uno::Int2 GetBackbufferSize(uGraphicsContext handle);
    static uGraphicsContext GetInstance();
    static int GetRealBackbufferHeight(uGraphicsContext handle);
};
// }

}}}} // ::g::Uno::Runtime::Implementation

redpajama_set_name: RedPajamaGithub


text:
Q: using linux header files in visual studio I was trying to use linux kernel header file on the visual studio 2013.
I want to do this for auto completion purpose.
I noticed that stdio.h file is inside of the C:\Program Files\Visual Studio 12.0\VC\crt\src,
So I copied my linux folder, which contains kernel header files, into the src folder.
However, Visual studio does not seem to find these header files.
For example:
#include <linux/kernel.h>
It says Error: cannot open source file "linux/kernel.h"
I tried to change all slash characters into back slash, however, it does not fix the issue.
What do I have to do if I want to make visual studio know this header file is existed?
I know I could move my kernel.h to my current folder and use #include "kernel.h"
However, I would like to keep the system header files in my computer and
use with #include <linux/kernel.h> when it is needed.

A: #include <kernel.h>

and add C:\Program Files\Visual Studio 12.0\VC\crt\src\linux to the include path (if one is using VS2017 which shipped with it).
To obtain the kernel.h file, i.e. kernel source, determine the kernel version one needs and obtain the src from kernel.org, e.g. 5.4.26

A: In Visual Studio 2015, the alternative is to install the Visual C++ for Linux Development and the Visual C++ for Android Development templates. At time of writing the Linux headers are only present in the Android development folder, on my machine it was C:\ProgramData\Microsoft\AndroidNDK64\android-ndk-r10e\platforms\android-21\arch-x86_64\usr\include. Add that path to the include path and Intellisense works for common Linux files like <sys/socket.h>.

A: Current location(s) under VS 2017 with Android files in a separate tree, 32 and 64 bit:
C:\Microsoft\AndroidNDK{,64}\android-ndk-r{NDK_VER}c\platforms\android-{P_VER}\arch-x86{,_64}\usr\include

NDK_VER -- versions of the NDK, currently 12,13,15
P_VER   -- target android platform version (aka level), currently the highest is 26

Examples:
C:\Microsoft\AndroidNDK\android-ndk-r15c\platforms\android-26\arch-x86\usr\include
C:\Microsoft\AndroidNDK\android-ndk-r15c\platforms\android-26\arch-x86_64\usr\include
C:\Microsoft\AndroidNDK64\android-ndk-r15c\platforms\android-26\arch-x86\usr\include
C:\Microsoft\AndroidNDK64\android-ndk-r15c\platforms\android-26\arch-x86_64\usr\include
This reflects general "new style" in VS with build platforms and target platforms being separated and orthogonal. There are also arch-{arm,mips}{,64} so 6 folders under arch target platform version.
Include files are the same in AndroidNDK and AndroidNDK64 and under one NDK version only files under machine and asm folders are different (for Intel and Mips even files under asm are identical for 32 and 64 bits).

redpajama_set_name: RedPajamaStackExchange


text:
Maharashtra shocker: Nine members of two brothers' families commit suicide
20 Jun, 2022, 11:40 am
Sangli, June 20, 2022
In a chilling incident, at least nine members of two brothers' families allegedly consumed poison and ended their lives in Mhaisal village near Miraj, police said here on Monday.
Among the victims are a veterinarian and his brother, a school teacher, their spouses and children, whose 9 bodies were recovered from their respective homes.
The motives behind the drastic step, whether it was planned or spontaneous or the kind of toxic substances they have consumed are not known immediately, and more details are awaited.
The news of the alleged mass-suicide spread like wildfire with scores of shocked people rushing to the homes in Ambika Nagar area of the village.
Top police officials, including Sangli Superintendent of Police Dikshitkumar Gedam, Mhaisal Police Inspector Chandrakant Bendre and others, rushed there to investigate and calm the locals.
The work of recording the panchnamas, taking photographs of the bodies before sending them for autopsy and other procedures is currently underway, said an official
Nine members of two brothers' families


text:
I.D.E.A. Scholarship
Inclusion, Diversity, Equity & Accessibility
ISMAR 2022 is striving towards an inclusive and accessible environment to encourage conference participation by individuals of all identities and with diverse backgrounds.
We value inclusive diversity in all forms, including but not limited to: age, race, ethnicity, culture, religious beliefs, language, socioeconomic status, citizenship, national origin, physical appearance, gender, marital status, sexual orientation, and physical abilities. We also acknowledge the historical barriers for limiting the access and participation of some groups. It is our belief that a diverse community is important to ensure representation in the development of technology that matters to a global society.
In this context, we invite early career researchers (early professors, undergraduate students, graduate students, and postdocs) to apply for the 2022 Inclusion, Diversity, Equity, and Accessibility (IDEA) Scholarship.
Eligible applicants are early-career researchers (early professors, undergraduate students, graduate students, and postdocs) from underrepresented or historically marginalized groups. These groups may include (but are not exclusive to):
Indigenous persons
People who identify as LGBTQIA+
Individuals from developing countries*
We also invite researchers from regions and countries historically under-represented at the ISMAR conference to apply.
The countries that are eligible to receive a developing countries registration grant are: any country in Latin America, Africa, Asia (excluding developed countries like China, Singapore, Korea and Japan) and the Middle East (excluding Israel, Saudi Arabia, UAE, Kuwait). Countries in eastern Europe will also be considered.
This year, there are four different types of grants, and applicants should apply for them depending on their needs.
1) Full registration reimbursement for online attendance;
2) Full registration reimbursement for in-person attendance;
3) Partial registration reimbursement for in-person attendance;
4) Partial registration reimbursement for online attendance;
In addition, we might provide up to $500 reimbursement for travel expenses (hotel, airfare, etc.) for in-person participation. This will be a case-by-case analysis, so please make sure to explain in detail how this scholarship would help you to attend ISMAR.
The 2022 IDEA Scholarship Committee will review applications based on eligibility, need, and impact. Given that we have a limited number of grants, you will also need to submit an updated copy of your CV (max 2 pages), briefly describe your background and why you would like to attend the 2022 ISMAR, and briefly explain how this scholarship will help you attend the conference.
Interested individuals may apply via this form.
The deadline for applications is September 24, 2022. The deadline is 23:59:59 AoE (Anywhere on Earth) == GMT/UTC-12:00, no matter where the submitter is located.
Recipients of the scholarship will be informed by October 01, 2022.
All identifiable information provided by applicants and sign-ups will be accessible only to members of the Inclusion, Diversity, Equity and Accessibility Committee. This information will be used for selection purposes.
After September 25th, all data will be de-identified and anonymized by the Inclusion, Diversity, and Accessibility Committee, with identifying markers being destroyed (deleted). This anonymized data will then be used for planning future iterations of ISMAR for statistical purposes. This anonymized data helps us understand how many applicants to plan for, what countries are underrepresented, the kinds of accessibility resources we need to provide, etc.
Applicants can request for data corrections or for removal of their data from the pool until September 25th by contacting Nayara Faria at nfaria@vt.edu.
This program is an initiative of the 2022 ISMAR Inclusion, Diversity, Equity and Accessibility Committee, and supported by the IEEE VGTC. The committee can be reached via email at diversity_chairs[a]ismar2022.org
If you are interested in supporting the Inclusion, Diversity and Accessibility Scholarship Program at 2022 ISMAR, please contact diversity_chairs[at]ismar2022.org


text:
\section{Introduction}
\label{AdSFLRWintro}

The gauge/gravity duality (see, e.g., \cite{Ammon:2015wua} for a recent review) is currently established as a valuable tool to approach the physics of strongly coupled quantum systems. The general idea is that, by mapping certain quantum systems to an equivalent dual gravity theory living in a higher dimensional bulk spacetime, difficult problems may become tractable. The duality has found a wide range of applications over the last years, specially when it comes to the nonequilibrium dynamics of quantum field theories at strong coupling, which tipically involves time-dependent solutions on the gravity side. Examples include the thermalization of non-Abelian plasmas similar to the quark gluon plasma formed in heavy ion collisions at the RHIC and LHC, which is mapped to an Anti de Sitter (AdS) black hole formation process on the gravity side \cite{Chesler:2008hg,Chesler:2010bi,Balasubramanian:2010ce,Heller:2011ju,Camilo:2014npa,Keegan:2015avk}, and the quench dynamics of quantum systems, where a time-dependent coupling (or \emph{quench}) on the field theory side translates into a boundary condition for bulk fields in the dual gravity description \cite{Das:2011nk,Buchel:2013lla,Buchel:2013gba,Buchel:2014gta,Camilo:2015wea}.

The Friedmann-Lemaître-Robertson-Walker (FLRW) metric corresponds to the most general spacetime exhibiting spatial homogeneity and isotropy. In $4$ dimensions, the metric can be written as
\begin{equation}
 ds^2 = -dt^2 + a(t)^2d\Omega_k^2\ ,
\end{equation}
where $a(t)$ is called the scale factor and $d\Omega_k^2=\frac{d\rho^2}{1-k\rho^2}+\rho^2(d\theta^2+\sin^2\theta d\phi^2)$ is the $3$-dimensional spatial metric of a constant curvature space. The spatial curvature $k$ can be positive, negative, or zero, and without loss of generality we can set its possible values to be $k=+1,0,-1$ corresponding to a unit sphere, Euclidean space, or unit hyperbolic space, respectively. The FLRW metric describes an expanding (contracting) spacetime provided that $a(t)$ is a monotonically increasing (decreasing) function. It is largely used in cosmology due to the observation that our universe is homogeneous and isotropic (with $k=0$) in cosmological scales \cite{Dodelson:2003ft}.

The FLRW spacetime also provides a good prototype to approach the nonequilibrium dynamics of an expanding system. It is well known, for instance, that even a locally static fluid flow characterized by the $4$-velocity $u^\mu=(1,0,0,0)$ in the FLRW metric has a nonvanishing expansion rate $\nabla_\mu u^\mu=3H(t)$ ($H(t)\equiv\frac{\dot{a}(t)}{a(t)}$ is the so-called Hubble parameter) due to the dynamical nature of the geometry itself. In spite of the time dependence, the high degree of spatial symmetry of the metric may render certain problems technically feasible. An interesting example is \cite{Bazow:2015dha}, where an analytical solution to the general relativistic Boltzmann equation in FLRW has been found describing the dynamics of an expanding massless gas with constant cross section.

In the present work, we use an expanding FLRW spacetime as the background arena in which to study a strongly coupled field theory plasma. In particular, we shall focus on a conformal field theory (CFT) with a holographic dual and resort to gauge/gravity duality methods in order to extract information about the expanding CFT plasma. An advantage of the holographic approach is that non-equilibrium quantities of the expanding plasma such as the
entropy density can be naturally associated with the
gravitational entropy of the apparent horizon on the gravity side \cite{Figueras:2009iu}. The crucial step here involves setting the Anti de Sitter (AdS) conformal boundary to take a FLRW form instead of the commonly used static boundaries. This is in principle possible since the boundary metric belongs to a conformal class, and one can switch between members of this class by appropriate bulk diffeomorphisms.

Previous efforts in this direction have been made in \cite{Apostolopoulos:2008ru} (see also \cite{Lamprou:2011sa,Tetradis:2009bk,Nojiri:2002hz}) using Fefferman-Graham coordinates, but were restricted basically to pure Einstein gravity in the bulk. We propose here a different foliation of AdS$_5$ black hole spacetimes using Eddington-Finkelstein-like coordinates such that the asymptotic boundary becomes the $4$-dimensional FLRW spacetime. The holographic dual picture is, therefore, that of a thermalized CFT on an expanding background, even though the bulk solution is not truly dynamical. The procedure is simple and applies equally well to a variety of AdS black holes, supported by external fields or not, leading to the same results of \cite{Apostolopoulos:2008ru} when applied to the AdS-Schwarzschild solution.

The paper is organized as follows. In Section \ref{sec:AdSFLRWgeneral} we introduce our FLRW foliation of generic AdS black holes, discuss the entropy production by the dual expanding plasma and set the ground to discuss holographic renormalization and one-point functions in the sequence. In Section \ref{sec:AdSFLRWexamples} we give three explicit examples, namely for the AdS-Schwarzschild, AdS-Gauss-Bonnet, and AdS-Reissner-Nordström solutions, calculate the corresponding renormalized one-point functions of the dual CFT and discuss the conformal anomalies. Section \ref{sec:AdSFLRWconclusions} contains the closing remarks.

\section{AdS black holes with a FLRW boundary}\label{sec:AdSFLRWgeneral}

We begin with a generic asymptotically AdS$_5$ black hole written in the usual form
\begin{equation}\label{eq:BHmetricusual}
ds^2 = -f(r)dt^2+f(r)^{-1}dr^2+\Sigma(r)^2d\Omega_k^2\ ,
\end{equation}
where $d\Omega_k^2$ denotes the metric of the horizon, corresponding to a spherical, planar, or hyperbolic horizon for $k=+1,0,-1$ respectively. The blackening factor $f(r)$ and the function $\Sigma(r)$ are left completely general with the only assumption that $f(r)\sim\frac{r^2}{L^2}$ and $\Sigma(r)\sim\frac{r}{L}$ for large $r$, as required in order to have AdS asymptotics with curvature radius $L$.\footnote{Of course the zero temperature cases of Poincaré and global AdS are also included in this class and, incidentally, will be included in our analysis. However, we shall ignore them since we are interested only in CFTs at finite $T$.} The event horizon $r_h$ is defined by (the largest root of) $f(r_h)=0$ and the corresponding Hawking temperature is $T=|f'(r_h)|/4\pi$. There may eventually be matter fields supporting the geometry, but for our purposes at this section they will play no role.

The first step involves going to the so-called ingoing Eddington-Finkelstein coordinates ($v,r$). This is done by trading the time coordinate $t$ to a new coordinate $v$ adapted to ingoing null geodesics, which is defined by $dv=dt+f(r)^{-1}dr$. The metric then reads
\begin{equation}\label{eq:BHmetricEF}
ds^2 = 2dvdr - f(r)dv^2 + \Sigma(r)^2d\Omega_k^2\ .
\end{equation}
Notice that the large $r$ behavior of the metric is $ds^2 \sim 2dvdr + \frac{r^2}{L^2}[- dv^2 + d\Omega_k^2]$, from where it is clear that the $4$-dimensional conformal boundary at $r=\infty$ (where the dual CFT lives) is the Einstein static universe $\mathbb{R}\times\Sigma_k$ with metric\footnote{The time coordinates $v$ and $t$ coincide at fixed-$r$ surfaces.}
\begin{equation}\label{eq:ESUk}
 ds_0^2 = g_{\mu\nu}^{(0)}dx^\mu dx^\nu = -dt^2+d\Omega_k^2\ .
\end{equation}
When $k=0$ this is just the $4$-dimensional Minkowski spacetime, which is by far the most studied one in holographic applications since most field theories of physical interest live in flat spacetime. In spite of that, for the sake of completeness we shall keep the spatial curvature $k$ arbitrary in the sequence.

Before proceeding it is instructive to recall a simple reason why the AdS conformal boundary indeed goes well with the intuitive notion of a boundary. This can be seen by calculating the time interval $\Delta v(r_0)$ spent by an outgoing light ray to travel radially from $r_0>r_h$ to the boundary at $r=\infty$ and back to $r_0$. It follows immediately from the definition of outgoing null geodesics in \eq{BHmetricEF}, $2dr-f(r)dv=0$, that
\begin{equation}
 \Delta v(r_0) = 4 \int_{r_0}^\infty\ \frac{dr'}{f(r')} < \infty\ ,
\end{equation}
which is obviously finite since there are no poles in the denominator for $r_0>r_h$ and the integrand vanishes at large $r'$.

In the following we shall introduce a different foliation of the black hole spacetime \eq{BHmetricEF} in such a way that the corresponding conformal boundary takes the form of a FLRW spacetime, namely
\begin{equation}\label{eq:FLRWk}
 ds_0^2 = g_{\mu\nu}^{(0)}dx^\mu dx^\nu = -dt^2+a(t)^2 d\Omega_k^2\ .
\end{equation}

In order to achieve that one needs two further coordinate transformations. We first define a new time coordinate $V$ with respect to which the old $v$ is a \lq\lq conformal time\rq\rq~with scale factor $a(V)$, i.e., $dv=\frac{dV}{a(V)}$, where $a(V)$ is assumed to be everywhere continuous and non-vanishing.
Finally, we introduce a new radial coordinate $R$ defined as $R=\frac{r}{a(V)}$. After plugging $dv=\frac{dV}{a}$ and $dr=a(V)dR+R\dot{a}(V)dV$ the metric \eq{BHmetricEF} becomes
\begin{eqnarray}\label{eq:BHmetricFLRW}
ds^2 &=& 2\frac{dV}{a}(adR+R\dot{a}dV)-f(Ra)\frac{dV^2}{a^2}+\Sigma(Ra)^2d\Omega_k^2\nonumber\\
&=& 2dVdR-\left[\frac{f(Ra)}{a^2}-2R\frac{\dot{a}}{a}\right]dV^2+\Sigma(Ra)^2d\Omega_k^2
\end{eqnarray}
This form is the one we are interested in this work. Note that the metric is still expressed in Eddington-Finkelstein-like coordinates (in the sense that $V$ is still adapted to null geodesics), but now it carries an artificial time dependence reminiscent of the transformation from $v$ to $V$. At large $R$ we have $f(Ra)\sim\frac{(Ra)^2}{L^2}$ and $\Sigma(Ra)\sim\frac{Ra}{L}$ due to our assumption of AdS asymptotics, and, therefore,
$$ds^2\sim 2dVdR+\frac{R^2}{L^2}[-dV^2+a(V)^2d\Omega_k^2]\ .$$
As a result, the new conformal boundary at $R=\infty$ has precisely the desired FLRW form \eq{FLRWk} with spatial curvature $k$ (the time coordinate is now called $V$). We shall refer to this as the \emph{cosmological boundary} just to remind that this is not the same as the commonly used AdS boundary at $r=\infty$.

Actually we shall pause for a moment here to argue that the cosmological boundary introduced above is indeed also compatible with the notion of a boundary. This is done by asking the same question asked previously for the AdS boundary, namely whether the time interval $\Delta V(R_0)$ spent by an outgoing light ray to go radially from $R_0$ to $\infty$ and back to $R_0$ in the metric \eq{BHmetricFLRW} is finite or not. The outgoing null geodesics in this case satisfy
\begin{equation}
 \frac{dR}{dV}=\frac{1}{2}\left[\frac{f(Ra)}{a^2}-2R\frac{\dot{a}}{a}\right] = \frac{1}{2}\left[\frac{R^2}{L^2}-2R\frac{\dot{a}}{a}+\cdots\right]\ .
\end{equation}
For simplicity we focus on the case of pure AdS space ($f(r)=\frac{r^2}{L^2}$), without loss of generality since this corresponds to the asymptotic structure of any AdS black hole. In this case the ellipsis in the previous expression is not present and it can be exactly integrated to yield
\begin{equation}
 R(V) = \frac{R_0a_0}{a(V)\left[1-\frac{R_0a_0}{2L^2}\int_{V_0}^V\ \frac{dV'}{a(V')}\right]}\ ,
\end{equation}
where we have introduced $R_0\equiv R(V_0)$ and $a_0\equiv a(V_0)$. The time $V_\infty$ corresponding to reaching the cosmological boundary $R=\infty$ is implicitly defined by
\begin{equation}
 \frac{R_0a_0}{2L^2}\int_{V_0}^{V_\infty}\ \frac{dV'}{a(V')}=1\ .
\end{equation}
A straightforward consequence of our assumption that the scale factor $a(V)$ is a continuous and everywhere non-vanishing function is that $V_\infty$ must be finite (although an explicit expression for it cannot be obtained without specifying the form of the scale factor). As a result, the time interval $\Delta V(R_0)=2(V_\infty-V_0)$ is guaranteed to be finite and, therefore, $R=\infty$ also provides a sensible notion of asymptotic boundary.

To summarize, we have introduced a different type of foliation for $5$-dimensional AdS black hole spacetimes of the form \eq{BHmetricusual} where the $4$-dimensional slices asymptotically approach the FLRW metric. This is very similar to the work done in \cite{Apostolopoulos:2008ru}. It should be stressed, however, that our procedure is astonishingly simpler and, in particular, our metric \eq{BHmetricFLRW} applies equally well for any AdS black hole (characterized by the functions $f,\Sigma$ and eventually matter fields\footnote{Of course matter fields when present must be changed according to the same coordinate transformations above to take a different $(V,R)$-dependent configuration that supports the FLRW-foliated metric \eq{BHmetricFLRW}. This is the case, e.g., for the AdS-Reissner-Nordström charged black hole (see Section \ref{sec:AdSFLRWexamples}).}), as we shall illustrate in the sequence, while the method of \cite{Apostolopoulos:2008ru} is hardly applicable beyond the simplest case of the AdS-Schwarzschild solution.

\subsection{Entropy production}\label{sec:EntropyProduction}

We begin our analysis by finding the location of the apparent horizon in our FLRW-foliated black hole metric \eq{BHmetricFLRW}.
The apparent horizon is formally defined as the outermost trapped surface, i.e., the closed null hypersurface on which all radially outgoing null geodesics have vanishing expansion (see e.g. \cite{booth:2005qc}). For a generic $5$-dimensional metric of the form $$ds^2=2dVdR-\alpha(V,R)dV^2+\beta(V,R)^2d\Omega_k^2$$ the expansion along outgoing null rays is given by $\theta_\text{out}\equiv\left(\partial_V+\frac{\alpha}{2}\partial_{R}\right)\ln\beta^3$ and the apparent horizon hence corresponds to the location $R_h(V)$ for which $\theta_\text{out} = 0$. For the case of interest \eq{BHmetricFLRW}, with $\alpha(V,R)=\frac{f(Ra)}{a^2}-2R\frac{\dot{a}}{a}$ and $\beta(V,R)=\Sigma(Ra)$, the result is
\begin{equation}\label{eq:apparenthorizonFLRWdef}
 \left[\partial_V\Sigma + \biggl(\frac{f(Ra)}{2a^2}-R\frac{\dot{a}}{a}\biggr)\partial_R\Sigma\right]\bigg|_{R=R_h} = 0\ .
\end{equation}
However, since $\Sigma$ only depends on $(V,R)$ through the combination $Ra(V)$, one can write $\partial_V\Sigma(Ra)=R\dot{a}\Sigma'(Ra)$, $\partial_R\Sigma(Ra)=a\Sigma'(Ra)$ (here a prime denotes the derivative with respect to the argument $Ra$) and, therefore, the definition of $R_h$ reduces to
\begin{equation}
 f(R_ha)\Sigma'(R_ha) = 0\ .
\end{equation}
For most black hole solutions of interest, which have $\Sigma(r)=\frac{r}{L}$ (see next section), the equation above gives simply $f(R_ha)=0$ or, equivalently, $R_h(V)=\frac{r_h}{a(V)}$, where the constant $r_h$ denotes the black hole event horizon in the standard coordinate system \eq{BHmetricEF} (i.e., $f(r_h)=0$). Nevertheless, if $\Sigma(r)$ has subleading contributions in $r$ of any kind such that $\Sigma'(r)$ is not constant, there may appear an additional horizon corresponding to $\Sigma'(R_ha)=0$.

Having determined its location, we now follow \cite{Figueras:2009iu} and associate the non-equilibrium entropy density $s$ of the expanding plasma living at the cosmological boundary with the Bekenstein-Hawking entropy of the apparent horizon, namely
\begin{equation}
 s = \frac{\Sigma(R_ha)^3}{4G_5}\ .
\end{equation}
From this it follows that, if $R_h=\frac{r_h}{a}$ is the only apparent horizon, then clearly
\begin{equation}
\frac{ds}{dV} = 0\ ,
\end{equation}
i.e., there is no entropy production by the plasma during the dynamical process. This matches the expectation from the hydrodynamics of conformally invariant fluids, for which there is no entropy production at all orders in the hydrodynamic expansion (see \cite{Buchel:2016cbj}). However, if the bulk solution admits another apparent horizon corresponding to the root of $\Sigma'(R_ha)$, then there may be a nonzero entropy production by the plasma since the combination $R_ha$ on which $s$ depends will not necessarily be constant anymore. This is the case, for instance, for the $\mathcal{N}=2^*$ plasma studied in \cite{Buchel:2016cbj}.

Similarly, one can associate to the expanding plasma the local temperature
\begin{equation}\label{eq:LocalT}
 T(V) = \frac{T_H}{a(V)}\ ,
\end{equation}
where $T_H$ is the temperature of the corresponding static plasma (i.e., the Hawking temperature of the black hole). As argued in \cite{Apostolopoulos:2008ru}, this follows from the fact that the FLRW metric \eq{FLRWk} and the static boundary metric \eq{ESUk} are connected by a Weyl rescaling, i.e., $ds^2_{\text{FLRW}}=a(\eta)^2ds_0^2$ where $\eta\equiv\int{\tfrac{dt}{a}}$ is the conformal time. As a result, the local temperature of the plasma in FLRW and the equilibrium temperature $T_H$ of the static plasma must be linked by a rescaling. Since the Euclidean proper time period in FLRW
scales as $a$ according to the formula above, the temperature of the expanding plasma, being inversely related to the period, must scale as $a^{-1}$ with respect to $T_H$. Another way to see that is to recall that our new slicing does not change the physical content of the bulk solution, i.e., we still have the same static AdS black hole in thermal equilibrium with its Hawking radiation at temperature $T_H$. The difference now is that we have a new notion of boundary ($R=\infty$) that expands in time according to the scale factor $a(V)$, and a comoving observer sitting in there will experience a temperature appropriately corrected by $a$ that corresponds precisely to \eq{LocalT}.

\subsection{One-point functions}
We now follow the spirit of \cite{Apostolopoulos:2008ru} and, by assuming that
\emph{i)} the cosmological boundary is holographic;
\emph{ii)} the standard holographic renormalization procedure can be carried out in the same way in there as in the usual AdS boundary,
we proceed to calculate the one-point functions for the dual CFT operators living in the cosmological boundary, i.e., for CFTs in FLRW spacetime.

The first step involved is to find the Fefferman-Graham (FG) expansion of the bulk metric (and eventually matter fields) near the cosmological boundary, since knowledge of the FG coefficients determines the CFT correlators via the holographic dictionary. Namely, we need to put the metric \eq{BHmetricFLRW} in the FG form
\begin{equation}\label{eq:FGmetric}
ds^2 = \frac{L^2}{z^2}\left[dz^2 + g_{\mu\nu}(z,x)dx^\mu dx^\nu\right]
\end{equation}
(here $z\sim L^2/R$ such that the cosmological boundary is, in these coordinates, at $z=0$) and find the first few coefficients of the near boundary expansion of $g_{\mu\nu}$,
\begin{eqnarray}\label{eq:FGmetricasymptotic}
 g_{\mu\nu}(z,x) &=& g_{\mu\nu}^{(0)}(x) + z^2g_{\mu\nu}^{(2)}(x) +z^4\bigl(g_{\mu\nu}^{(4)}(x)+h_{\mu\nu}^{(4)}(x)\log z\bigr)+ \cdots\ ,
\end{eqnarray}
where the leading one, $g_{\mu\nu}^{(0)}(x)$, is the FLRW metric \eq{FLRWk}, and the subleading ones are determined by the bulk equations of motion.
A practical way to achieve that is to write generic coordinate transformations from ($V,R$) to FG coordinates ($x^0\equiv\tau,z$), i.e., $V=V(\tau,z)$ and $R=R(\tau,z)$, and then get the transformation equations by comparing our metric \eq{BHmetricFLRW} with \eq{FGmetric}. This leads to the following set of equations
\begin{eqnarray}\label{eq:VRtoFGeqs}
2\partial_z R\partial_z V-\alpha (\partial_z V)^2 &=& \frac{L^2}{z^2}\nonumber\\
\partial_z V\partial_\tau{R}+\partial_\tau{V}\partial_z R-\alpha \partial_z V\partial_\tau{V} &=& 0\ ,
\end{eqnarray}
which determine the precise form of the transformations, together with the FG metric components expressed in terms of $V$ and $R$, which can be massaged to take the simple form
\begin{equation}\label{eq:FGmetriccoeffsVR}
 g_{\tau\tau}=-\frac{(\partial_\tau{V})^2}{(\partial_z V)^2}\qquad g_{ij}dx^idx^j=\frac{z^2}{L^2}\Sigma^2d\Omega_k^2\qquad g_{\tau i}=0\ .
\end{equation}
The near-boundary solution to the transformation equations \eq{VRtoFGeqs} can be easily obtained to any desired order with a power series ansatz of the form
\begin{equation}\label{eq:VRtoFGsolgeneric}
V(\tau,z) = \sum_{n=0}V_n(\tau)z^n\qquad R(\tau,z) = \sum_{n=0}R_n(\tau)z^{n-1}
\end{equation}
with $V_0(\tau)\equiv\tau$ (such that $V$ and $\tau$ coincide at the boundary) and $R_0(\tau)\equiv L^2$ (such that $R=\frac{L^2}{z}+\cdots$). Once this solution is found, by plugging it back into \eq{FGmetriccoeffsVR} and expanding for small $z$ yields the desired FG asymptotic expansion \eq{FGmetricasymptotic}. One is then ready to obtain the corresponding one-point functions of the dual CFT living on the cosmological boundary using standard holographic renormalization.

So far the analysis has been quite general. We shall now illustrate the procedure by particularizing the functions $f(r),\Sigma(r)$ to a few black holes of physical interest.

\section{Examples}\label{sec:AdSFLRWexamples}

\subsection{AdS-Schwarzschild black hole}

The AdS-Schwarzschild black hole is an exact static solution to pure Einstein gravity with a negative cosmological constant $\Lambda=-12/L^2$ in the bulk, namely
\begin{equation}
 S = \frac{1}{16\pi G_5}\int\ d^5x\sqrt{-g}\left[R+\frac{12}{L^2}\right].
\end{equation}
The solution with horizon curvature $k$ corresponds to a metric of the form \eq{BHmetricusual} with $f(r)$ and $\Sigma(r)$ given by
\begin{equation}
 f(r) = \frac{r^2}{L^2}\left(1+\frac{kL^2}{r^2}-\frac{M}{r^4}\right)\qquad \Sigma(r)=\frac{r}{L}\ ,
\end{equation}
where the mass $M$ is related to the event horizon radius $r_h$ according to
$M = r_h^4\left(1+\frac{kL^2}{r_h^2}\right)$.
Its corresponding Hawking temperature is readily found to be
\begin{equation}\label{eq:HawkingTSAdS5k}
 T_H = \frac{kL^2+2r_h^2}{2\pi L^2r_h}\ .
\end{equation}

The explicit form of the foliation \eq{BHmetricFLRW} for the AdS-Schwarzschild black hole reads
\begin{eqnarray}\label{eq:SAdSmetricFLRW}
 ds^2 &=& 2dVdR-\left[\frac{R^2}{L^2}\left(1+\frac{kL^2}{R^2a^2}-\frac{M}{R^4a^4}\right)-2R\frac{\dot{a}}{a}\right]dV^2+\frac{R^2a^2}{L^2}d\Omega_k^2\ .
\end{eqnarray}
If the standard holographic dictionary extrapolates to the cosmological boundary $R=\infty$, this metric would be the holographic dual of a $\mathcal{N}=4$ SYM plasma in the FLRW metric \eq{FLRWk} with spatial curvature $k$. As discussed in Section \ref{sec:EntropyProduction}, one can associate to this nonequilibrium plasma the local temperature \eq{LocalT}, namely
\begin{equation}\label{eq:localHawkingTSAdS5k}
 T(V)=\frac{kL^2+2r_h^2}{2\pi L^2r_ha}\ .
\end{equation}
In the following for the sake of simplicity we take $L=1$.

It is worth mentioning that the metric above in the planar case ($k=0$) has been previously used by the authors of \cite{Buchel:2016cbj} as the starting point to study the $\mathcal{N}=2^*$ plasma close to conformality in a FLRW spacetime.\footnote{We emphasize that, although not obvious, this is nothing but AdS-Schwarzschild expressed in unusual coordinates.}

The transformation \eq{VRtoFGsolgeneric} from our ($V,R$) coordinates to the Fefferman-Graham system ($\tau,z$) is given asymptotically by
\begin{eqnarray}\label{eq:VRtoFGsolSAdS}
V(\tau,z) &=& \tau -z +\frac{-2a\ddot{a}+\dot{a}^2+k}{12a^2}z^3 +\frac{a^2 \dddot{a}+\dot{a}^3+\dot{a}\left(k-2 a\ddot{a}\right)}{24a^3}z^4 \notag\\ &&+\frac{3\dot{a}^4-2{a}^{(4)}a^3-3\left(k^2+6M\right)+2a\ddot{a}\left(5k-\dot{a}^2\right)+a^2\left(6\dddot{a}\dot{a}-8\ddot{a}^2\right)}{240a^4}z^5 + \cdots\notag\\
R(\tau,z) &=& \frac{1}{z} + \frac{\dot{a}}{a} - \frac{2a\ddot{a}-3\dot{a}^2+k}{4a^2}z + \frac{a^2\dddot{a}+4\dot{a}^3-\dot{a}\left(5a\ddot{a}+2k\right)}{6a^3}z^2 \notag\\
&&+ \frac{13\dot{a}^4-a^3{a}^{(4)}-11k\dot{a}^2+a\ddot{a}\left(5k-21\dot{a}^2\right)+a^2\left(2\ddot{a}^2+7\dddot{a}\dot{a}\right)+3M}{24a^4}z^3 + \cdots\notag\\
\end{eqnarray}
with $a$ and its derivatives now viewed as functions of $\tau$. From \eq{FGmetriccoeffsVR} it then follows that the Fefferman-Graham expansion \eq{FGmetricasymptotic} of the metric in this case has the following non-null coefficients
\begin{align}\label{eq:FGcoeffsSAdS}
&g_{\tau\tau}^{(0)} = -1\notag\\
&g_{\tau\tau}^{(2)} = -\frac{\dot{a}^2-2a\ddot{a}+k}{2a^2}\notag\\
&g_{\tau\tau}^{(4)} = -\frac{\dot{a}^4+4a^2 \ddot{a}^2+2\dot{a}^2(k-2a\ddot{a})-4ka\ddot{a}+k^2-12M}{16a^4}\notag\\
&g_{ij}^{(0)}dx^idx^j = a^2d\Omega_k^2\notag\\
&g_{ij}^{(2)}dx^idx^j = -\frac{\dot{a}^2+k}{2}d\Omega_k^2\notag\\
&g_{ij}^{(4)}dx^idx^j = \frac{2k\dot{a}^2+\dot{a}^4+k^2+4 M}{16a^2}d\Omega_k^2\ .
\end{align}

The holographic renormalization for pure Einstein gravity in the bulk has been done in \cite{deHaro:2000vlm}, to which we refer the reader for details. The resulting expression for the renormalized energy-momentum tensor of the dual CFT living on the boundary with metric $g^{(0)}$ is generically given by
\begin{eqnarray}\label{eq:TmunuCFTeinstein}
\langle T_{\mu\nu}\rangle &=& \frac{1}{ 4\pi G_5}\left\{g^{(4)}_{\mu\nu}-\frac{1}{2}g^{(2)\sigma}_{\ \mu}g^{(2)}_{\sigma\nu}
+\frac{1}{4}\bigl(g^{(2)\sigma}_{\ \sigma}\bigr) g^{(2)}_{\mu\nu}-\frac{1}{8}\bigl[\bigl(g^{(2)\sigma}_{\ \sigma}\bigr)^2-g^{(2)}_{\sigma\rho}g^{(2)\rho\sigma}
\bigr]g^{(0)}_{\mu\nu}\right\}\ ,
\end{eqnarray}
where indices are to be raised and lowered with the boundary metric $g^{(0)}$.
In our case, with the FG coefficients \eq{FGcoeffsSAdS}, this yields the following energy density $\mathcal{E}\equiv \langle T_{\tau\tau}\rangle$ and pressure $\mathcal{P}\equiv \langle T_{\ i}^{i}\rangle$ (no summation over $i$ implied) for the $\mathcal{N}=4$ SYM plasma
\begin{eqnarray}\label{eq:CFTenergypressureSAdS}
\mathcal{E} &=& \frac{3(\dot{a}^2+k)^2+12M}{64\pi G_5 a^4} \nonumber\\
\mathcal{P} &=& \frac{(\dot{a}^2+k)^2+4M-4a\ddot{a}(\dot{a}^2+k)}{64\pi G_5 a^4}\ ,
\end{eqnarray}
in perfect agreement with the results of \cite{Apostolopoulos:2008ru}. These expressions can be cast entirely in $4$-dimensional CFT language by expressing the mass parameter $M = r_h^4\left(1+\frac{kL^2}{r_h^2}\right)$ in terms of the local temperature $T$ of the plasma using \eq{localHawkingTSAdS5k} and the $5$-dimensional Newton constant $G_5$ in terms of the number of colors $N_c$ via the standard AdS$_5$/CFT$_4$ relation $G_5=\frac{\pi L^3}{2N_c^2}$. For instance, in the $k=0$ case, with $M=(\pi aT)^4$ we obtain
\begin{eqnarray}\label{eq:CFTenergypressureSAdSin4dlanguagek=0}
\mathcal{E} &=& \frac{3N_c^2T^4}{8}+\frac{3N_c^2}{32\pi^2}\frac{\dot{a}^4}{a^4}\nonumber\\
\mathcal{P} &=& \frac{\mathcal{E}}{3}-\frac{N_c^2}{8\pi^2}\frac{\ddot{a}\dot{a}^2}{a^3}\ .
\end{eqnarray}

It interesting to note that when $a(V)\equiv1$ (where $R=\infty$ becomes the usual AdS boundary $r=\infty$) we get the expected conformal plasma in $\mathbb{R}\times\Sigma_k$ with $\mathcal{E}=3\mathcal{P}$, while the presence of a non-constant scale factor breaks the conformal invariance leading to a conformal anomaly given by
\begin{equation}\label{eq:CFTanomalySAdS}
 \langle T_{\ \mu}^{\mu}\rangle = 3\mathcal{P}-\mathcal{E} = -\frac{3\ddot{a}(\dot{a}^2+k)}{16\pi G_5 a^3}\ .
\end{equation}
The anomaly has a clearly geometric nature due exclusively to the nontrivial rate of cosmological expansion. For an expanding plasma ($\ddot{a}>0$) in flat space or in a sphere this quantity is strictly negative.

\subsection{AdS-Gauss-Bonnet black hole}

We start by reviewing the Einstein-Gauss-Bonnet action in $5$ dimensions. It consists in one of the simplest generalizations of Einstein gravity built from higher derivative terms in the action that still yield second order equations of motion for the metric.\footnote{In fact, the Einstein-Gauss-Bonnet action is just a very special case of the so-called \emph{Lovelock gravity}, which is the most general metric theory of gravity giving rise to second order equations of motion (see \cite{Padmanabhan:2013xyr} for a review).} With the inclusion of a negative cosmological constant $\Lambda\equiv-12/L^2$, the action is
\begin{eqnarray}\label{eq:EGBaction}
S &=& \frac{1}{16\pi G_5}\int d^5x\sqrt{-g}\Big[R+\frac{12}{L^2}+\frac{L^2}{2}\lambda_{_\text{GB}}(R_{abcd}R^{abcd}-4R_{ab}R^{ab}+R^2)\Big],
\end{eqnarray}
where $\lambda_{_\text{GB}}$ is the Gauss-Bonnet parameter. It is still unclear at the moment whether a higher curvature correction of the Gauss-Bonnet type \eq{EGBaction} can be obtained from a top-down string theory construction: the leading $\alpha'$ corrections to the action of Type IIB supergravity, corresponding to finite 't Hooft coupling corrections to the dual $\mathcal{N}=4$ SYM theory, are known to take the form of more complicated higher curvature terms schematically of the form $\alpha'^3R^3$ \cite{Grisaru:1986vi}. Nevertheless, the general belief is that it may provide qualitative information into properties shared by generic higher curvature terms, with the practical advantages of being tractable and having a number of exact solutions available in the literature.

The action \eq{EGBaction} has been extensively studied in the context of holography. Interestingly, the presence of the extra Gauss-Bonnet coupling $\lambda_{_\text{GB}}$ in the bulk allows for a holographic dual CFT with two distinct central charges $c\ne b$ \cite{Nojiri:1999mh,Blau:1999vz}.\footnote{We denote here the second central charge by $b$ instead of the commonly used $a$ in order to avoid confusion with the scale factor $a(V)$ appearing throughout the paper.} Namely, the central charges, defined in the standard way via the conformal anomaly as
\begin{equation}\label{eq:GBcentralchargesdef}
 \langle T_{\ \mu}^{\mu}\rangle = \frac{1}{16\pi^2}(cW-bE)\ ,
\end{equation}
are related to $\lambda_{_\text{GB}}$ and the other gravitational parameters via \cite{deBoer:2011wk}
\begin{eqnarray}\label{eq:GBcentralchargesdef2}
c &=& \frac{\pi L_\text{AdS}^3}{8G_5}\sqrt{1-4\lambda_{_\text{GB}}} \notag\\
b &=& \frac{\pi L_\text{AdS}^3}{8G_5}\bigl(-2+3\sqrt{1-4\lambda_{_\text{GB}}}\bigr)\ .
\end{eqnarray}
The AdS radius appearing above depends on $\lambda_{_\text{GB}}$
(see below for details), while the quantities
$W\equiv W_{\mu\nu\rho\sigma}W^{\mu\nu\rho\sigma}$ and $E\equiv\mathcal{R}_{\mu\nu\sigma\rho}\mathcal{R}^{\mu\nu\sigma\rho}-4\mathcal{R}_{\mu\nu}\mathcal{R}^{\mu\nu}+\mathcal{R}^2$ are respectively the squared Weyl tensor and the Euler density associated with the $4$-dimensional metric where the CFT lives. In the Einstein gravity limit $\lambda_{_\text{GB}}=0$ the two central charges collapse to a single one $c=b\sim N_c^2$ and the $SU(N_c)$ $\mathcal{N}=4$ SYM theory is recovered consistently.

The AdS-Gauss-Bonnet black hole with horizon curvature $k$ is an exact static spherically symmetric solution to the equations of motion of \eq{EGBaction}, first obtained in \cite{Cai:2001dz}. The metric has the standard black hole form \eq{BHmetricEF} with
\begin{eqnarray}
 f(r) &=& k + \frac{r^2}{2L^2\lambda_{_\text{GB}}} \left[1-\sqrt{1-4\lambda_{_\text{GB}}\left(1-\frac{ML^2}{r^4}\right)}\ \right]\notag\\
 \Sigma(r)&=&\frac{r}{L}\ ,
\end{eqnarray}
where $M$ is a parameter related to the black hole mass that can be conveniently expressed in terms of the event horizon location $r_h$ as $$M\equiv r_h^4\left(\frac{1}{L^2} + \frac{k}{r_h^2}+\lambda_{_\text{GB}} \frac{L^2k^2}{r_h^4}\right)\ .$$
The Hawking temperature associated to this solution reads
\begin{equation}\label{eq:localHawkingTGBAdS5k}
T_H = \frac{r_h(2r_h^2+kL^2)}{2\pi L^2(r_h^2+2kL^2\lambda_{_\text{GB}})}\ .
\end{equation}

It is worth noticing that the AdS-Gauss-Bonnet is an asymptotically AdS black hole, i.e., $f(r)\sim\frac{r^2}{L_{_\text{AdS}}^2}$ for large $r$. However, the AdS curvature radius is shifted from the usual $L$ to an effective radius $L_\text{AdS}$ due to the presence of $\lambda_{_\text{GB}}$, namely $L_\text{AdS}^2\equiv\frac{L^2}{2}(1+\sqrt{1-4\lambda_{_\text{GB}}})$. In particular, when the standard choice of units $L=1$ is made (which corresponds to making the cosmological constant $\Lambda=-12$) it should be kept in mind that the resulting AdS radius appearing in the metric is not unity.

Our FLRW foliation \eq{BHmetricFLRW} of the AdS-Gauss-Bonnet black hole metric takes the form
\begin{align}
ds^2 = 2dVdR+\frac{R^2a^2}{L_\text{eff}^2}d\Omega_k^2-\left\{\frac{k}{a^2}+\frac{R^2}{2L^2\lambda_{_\text{GB}}}\bigg[1-\sqrt{1-4\lambda_{_\text{GB}}\Big(1-\frac{ML^2}{R^4a^4}\Big)}\bigg]-2R\frac{\dot{a}}{a}\right\}dV^2
\end{align}
where the spatial coordinates were conveniently redefined by appropriate factors so as to make $\frac{d\Omega_k^2}{L^2}\rightarrow\frac{d\Omega_k^2}{L_\text{AdS}^2}$ and, hence, have a canonically normalized FLRW boundary of the form \eq{FLRWk}. Just as in the AdS-Schwarzschild case (see previous section), the holographic dual expanding CFT plasma living at $R=\infty$ can be associated the local temperature $T(V)=\tfrac{T_H}{a(V)}$.

From now on we shall take $L=1$ and treat the Gauss-Bonnet parameter as small, working always to linear order in $\lambda_{_\text{GB}}$ for simplicity (hence all the formulas containing $\lambda_{_\text{GB}}$ below are valid up to $\mathcal{O}(\lambda_{_\text{GB}}^2)$ corrections, although we choose not to unnecessarily repeat this symbol in each and every expression). The transformation from ($V,R$) to the Fefferman-Graham coordinates ($\tau,z$) can be obtained precisely in the same way as before (the expressions are too cumbersome to be shown here, though),
from where we get the following FG metric coefficients
\begin{align}\label{eq:FGcoeffsGB}
g_{\tau\tau}^{(0)} &= -1\notag\\
g_{\tau\tau}^{(2)} &= -\frac{1}{2a^2}(1-\lambda_{_\text{GB}})\left(-2a\ddot{a}+\dot{a}^2+k\right) \notag\\
g_{\tau\tau}^{(4)} &= -\frac{1}{16a^4}\bigl[(1-2\lambda_{_\text{GB}})\bigl(4a\ddot{a}(a\ddot{a}-\dot{a}^2-k)+2k\dot{a}^2+\dot{a}^4+k^2\bigr)-12(1+\lambda_{_\text{GB}})M\bigr]\notag\\
g_{ij}^{(0)}dx^idx^j &= a^2d\Omega_k^2\notag\\
g_{ij}^{(2)}dx^idx^j &= -\frac{1}{2}(1-\lambda_{_\text{GB}}) \left(\dot{a}^2+k\right)d\Omega_k^2\notag\\
g_{ij}^{(4)}dx^idx^j &= \frac{1}{16a^2}\bigl[(1-2\lambda_{_\text{GB}})(2k\dot{a}^2+\dot{a}^4+k^2)+4(1+\lambda_{_\text{GB}})M\bigr]d\Omega_k^2\ .
\end{align}

The holographic renormalization of the Einstein-Gauss-Bonnet action \eq{EGBaction} has been carried out in detail in \cite{Liu:2008zf,Astefanesei:2008wz,Jahnke:2014vwa} to linear order in $\lambda_{_\text{GB}}$ (see also \cite{Brihaye:2008xu} for arbitrary $\lambda_{_\text{GB}}$).\footnote{We follow here the same conventions of \cite{Jahnke:2014vwa}. In particular, the Gauss-Bonnet parameter $\lambda_{_\text{GB}}$ used here differs from the $\alpha$ used in \cite{Liu:2008zf}, namely $\alpha\equiv\frac{L^2}{2}\lambda_{_\text{GB}}$.} The final expression for the boundary energy-momentum tensor can be expressed in terms of the Fefferman-Graham coefficients as
\begin{equation}
\langle T_{\mu\nu}\rangle =  \langle T_{\mu\nu}\rangle_{_\text{Einstein}} + \lambda_{_\text{GB}} \langle T_{\mu\nu}\rangle_{_\text{GB}}\ ,
\end{equation}
where the $\lambda_{_\text{GB}}=0$ contribution $\langle T_{\mu\nu}\rangle_{_\text{Einstein}}$ due to pure Einstein gravity is the same as in \eq{TmunuCFTeinstein}, while the first order Gauss-Bonnet correction $\langle T_{\mu\nu}\rangle_{_\text{GB}}$ reads
\begin{eqnarray}
 \langle T_{\mu\nu}\rangle_{_\text{GB}}  &=& \frac{1}{16\pi G_5}\bigl[
-4g^{(2)\sigma}_{\ \mu}g^{(2)}_{\nu\sigma} + 7g^{(2)\sigma}_{\ \sigma}g^{(2)}_{\mu\nu} - 6g^{(4)}_{\mu\nu} - g^{(2)}_{\sigma\rho} g^{(2)}{}^{\sigma\rho} g^{(0)}_{\mu\nu} - 2\bigl(g^{(2)\sigma}_{\ \sigma}\bigr)^2 g^{(0)}_{\mu\nu} \nonumber\\
&& + 6g^{(4)\sigma}_{\ \sigma} g^{(0)}_{\mu\nu} - 3h^{(4)}_{\mu\nu} + 3h^{(4)\sigma}_{\ \sigma} g^{(0)}_{\mu\nu} + \tfrac{13}{4} \mathcal{R}^{(0)} g^{(2)}_{\mu\nu} - 2\mathcal{R}^{(0)}g^{(2)\sigma}_{\ \sigma} g^{(0)}_{\mu\nu}\nonumber \\
&& + \tfrac{29}{2}{g^{(2)}}{}^{\sigma\rho}\mathcal{R}^{(0)}_{\mu\sigma\nu\rho} + 4g^{(2)\sigma}_{\ \sigma} \mathcal{R}^{(0)}_{\mu\nu} - \tfrac{53}{4}g^{(2)\sigma}_{\ \nu}\mathcal{R}^{(0)}_{\mu\sigma} - \tfrac{53}{4}g^{(2)\sigma}_{\ \mu}\mathcal{R}^{(0)}_{\nu\sigma} +  \tfrac{11}{4}{g^{(2)}}{}^{\sigma\rho}\mathcal{R}^{(0)}_{\sigma\rho} g^{(0)}_{\mu\nu}\nonumber \\
&& + \tfrac{37}{4}\nabla^{(0)}_{\nu}\nabla^{(0)}_{\mu}g^{(2)\sigma}_{\ \sigma} - \tfrac{37}{4}\nabla^{(0)}_{\mu}\nabla^{(0)}_{\sigma}g^{(2)\sigma}_{\ \nu} - \tfrac{37}{4}\nabla^{(0)}_{\nu}\nabla^{(0)}_{\sigma}g^{(2)\sigma}_{\ \mu} + \tfrac{5}{4}g^{(0)}_{\mu\nu} \nabla^{(0)}_{\rho}\nabla^{(0)}_{\sigma}{g^{(2)}}{}^{\sigma\rho}\nonumber \\
&& + \tfrac{37}{4}\Box^{(0)}g^{(2)}_{\mu\nu} - \tfrac{5}{4}g^{(0)}_{\mu\nu}\Box^{(0)}g^{(2)\sigma}_{\ \sigma}\bigr]\ .
\end{eqnarray}
In the above the covariant derivatives $\nabla^{(0)}$ as well as the curvatures $\mathcal{R}^{(0)}$ are to be calculated with the boundary metric $g^{(0)}_{\mu\nu}$. In our case, inserting the FG coefficients \eq{FGcoeffsGB} and expanding to linear order in $\lambda_{_\text{GB}}$ results in the following energy density $\mathcal{E}\equiv \langle T_{\tau\tau}\rangle$ and pressure $\mathcal{P}\equiv \langle T_{\ i}^{i}\rangle$ of the dual CFT
\begin{eqnarray}\label{eq:CFTenergypressureAdSGB}
\mathcal{E} &=& \frac{3(\dot{a}^2+k)^2+12M}{64\pi G_5 a^4}-\frac{3\bigl[15(k+\dot{a}^2)^2+4M-64a\ddot{a}(k+\dot{a}^2-a\ddot{a})\bigr]}{128\pi G_5 a^4}\lambda_{_\text{GB}} \nonumber\\
\mathcal{P} &=& \frac{(\dot{a}^2+k)^2+4M-4a\ddot{a}(k+\dot{a}^2)}{64\pi G_5 a^4}-\frac{15(k+\dot{a}^2)^2+4M-4a\ddot{a}[31(k+\dot{a}^2)-16a\ddot{a}]}{128\pi G_5a^4}\lambda_{_\text{GB}}\ .\notag\\
\end{eqnarray}
Notice, in particular, that there is a conformal anomaly given by
\begin{eqnarray}\label{eq:CFTanomalyGBAdS}
 \langle T_{\ \mu}^{\mu}\rangle = 3\mathcal{P}-\mathcal{E} =  -\Bigl(1-\frac{15}{2}\lambda_{_\text{GB}}\Bigr)\frac{3\ddot{a}(k+\dot{a}^2)}{16\pi G_5 a^3}  \ ,
\end{eqnarray}
in agreement with the generic structure \eq{GBcentralchargesdef}.
Namely, the central charges $c$ and $b$ of \eq{GBcentralchargesdef2} when linearized in $\lambda_{_\text{GB}}$ read $c=\frac{\pi}{8G_5}\bigl(1-\tfrac{7}{2}\lambda_{_\text{GB}}\bigr)$ and $b=\frac{\pi}{8G_5}\bigl(1-\tfrac{15}{2}\lambda_{_\text{GB}}\bigr)$, which together with the expressions $W=0$ and $E=\frac{24\ddot{a}(k+\dot{a}^2)}{a^3}$ for the FLRW metric reduce the general expression \eq{GBcentralchargesdef} to \eq{CFTanomalyGBAdS}.

The results above generalize the expressions \eq{CFTenergypressureSAdS} and \eq{CFTanomalySAdS} obtained in the previous section to linear order in the Gauss-Bonnet parameter. They are believed to share qualitative features with the corresponding result for the $\mathcal{N}=4$ plasma including leading $1/\lambda$ corrections (here $\lambda=g_{_\text{YM}}^2N_c$ is the 't Hooft coupling). Once again one would like to emphasize that it follows naturally from our FLRW-like foliation \eq{BHmetricFLRW} of generic AdS spacetimes as a simple application to the AdS-Gauss-Bonnet black hole.

\subsection{AdS-Reissner-Nordström black hole}

We now turn to the case of a charged black hole in order to introduce a chemical potential for the dual plasma. This is the case, for instance, for the quark-gluon plasma of QCD which has a nonvanishing barion chemical potential. It is also interesting to illustrate how our procedure works when matter fields are present. The simplest bulk action includes a $U(1)$ gauge field minimally coupled to the Einstein-Hilbert action with a negative cosmological constant, namely
\begin{equation}
 S = \frac{1}{16\pi G_5}\int\ d^5x\sqrt{-g}\left[R+\frac{12}{L^2}-\frac{1}{4}F_{ab}F^{ab}\right]\ .
\end{equation}
An exact solution to the resulting Einstein and Maxwell equations is the AdS-Reissner-Nordström (AdSRN) black hole, a charged black hole whose metric can be cast in the standard black hole form \eq{BHmetricusual} with $f(r)$ and $\Sigma(r)$ given by (for simplicity we consider only the planar horizon case $k=0$)
\begin{equation}
 f(r) = \frac{r^2}{L^2}\left(1-\frac{M}{r^4}+\frac{Q^2}{r^6}\right)\qquad \Sigma(r)=\frac{r}{L}\ ,
\end{equation}
in addition to the nontrivial gauge field configuration
\begin{equation}\label{eq:RNAdSgaugefield}
 A_adx^a = \mu\left(1-\frac{r_h^2}{r^2}\right)dt\ .
\end{equation}
In the above we have conveniently expressed the solution in terms of four parameters, the mass $M$, charge $Q$, chemical potential $\mu$ and horizon radius $r_h$ (satisfying $f(r_h)=0$), but only two of them are independent parameters. For instance, $M$ and $Q$ can be eliminated in favor of $\mu$ and $r_h$ as
$$M = r_h^4+\frac{Q^2}{r_h^2}\ ,\qquad Q^2 = \frac{L^2\mu^2r_h^4}{3}\ .$$
The corresponding Hawking temperature is
\begin{equation}\label{eq:HawkingTRNAdS5k0}
 T_H = \frac{r_h}{\pi L^2}\left(1-\frac{L^2\mu^2}{6r_h^2}\right)\ .
\end{equation}

The AdSRN solution is believed to be holographically dual to a CFT plasma at temperature $T_H$ and chemical potential $\mu$ living at the AdS boundary $r=\infty$. Notice that there is a critical value for the chemical potential $\mu_c=\sqrt{6}r_h/L$ (correspondingly $Q_c=\sqrt{2}r_h^3$) where the temperature vanishes and the solution becomes extremal.

The explicit form of the foliation \eq{BHmetricFLRW} for the AdSRN black hole, including the corresponding ($V,R$)-dependent gauge field configuration needed to support the metric\footnote{Namely, a gauge field configuration originally of the form $A_adx^a=\phi(r)dt$ (such as \eq{RNAdSgaugefield}) after the sequence of coordinate transformations $dt=dv-f(r)^{-1}dr$, $dv=a(V)^{-1}dV$ and finally $r=Ra(V)$ becomes $$A_adx^a = \phi(Ra)\left[\left(\frac{1}{a}-\frac{R\dot{a}}{f(Ra)}\right)dV-\frac{a}{f(Ra)}dR\right].$$}, takes the following form
\begin{eqnarray}\label{eq:RNAdSmetricFLRW}
 ds^2 &=& 2dVdR-\left[\frac{R^2}{L^2}\Big(1-\frac{M}{R^4a^4}+\frac{Q^2}{R^6a^6}\Big)-2R\frac{\dot{a}}{a}\right]dV^2+\frac{R^2a^2}{L^2}d\mathbf{x}^2\notag\\
 A_adx^a &=& \mu\left(1-\frac{r_h^2}{R^2a^2}\right)\left(\frac{1}{a}-\frac{L^2\dot{a}/Ra^2}{1-\frac{M}{R^4a^4}+\frac{Q^2}{R^6a^6}}\right)dV-\mu\left(1-\frac{r_h^2}{R^2a^2}\right)\frac{L^2/R^2a}{1-\frac{M}{R^4a^4}+\frac{Q^2}{R^6a^6}}dR,\qquad
\end{eqnarray}
where we have used $d\mathbf{x}^2$ to denote the spatial part $d\Omega_{k=0}^2$. As before, the local temperature $T(V)$ of the holographic dual nonequilibrium plasma is given by \eq{LocalT}.

It is interesting to notice that at the cosmological boundary $R=\infty$ what remains of the gauge field above is
\begin{equation}
 A_\nu dx^\nu\big|_{_\text{bdry}} = \frac{\mu}{a}dV\ ,
\end{equation}
showing that the CFT plasma living in there has a time-dependent chemical potential $\tilde{\mu}(V)\equiv\frac{\mu}{a(V)}$.  Interestingly, by reversing the logic, one learns the important lesson that a CFT plasma subject to a time-dependent chemical potential $\tilde{\mu}(V)$ (what is sometimes referred to as a \emph{quench} in the chemical potential) experiences a non-equilibrium dynamics equivalent to a cosmological evolution with the scale factor being inversely related to the \lq\lq quench profile\rq\rq, i.e., $a(V)\sim1/\tilde{\mu}(V)$.

The AdSRN metric \eq{RNAdSmetricFLRW} parametrized by ($M,Q$) differs from the AdS-Schwarzschild solution \eq{SAdSmetricFLRW} only due to the presence of the charge $Q$, which comes with a subleading $1/R$ dependence and, thus, is expected to play a significant role only sufficiently deep inside the bulk spacetime. This suggests that the first terms in the Fefferman-Graham expansion of AdSRN near the cosmological boundary at $R=\infty$ should not differ from those obtained before. In fact, one can check explicitly that the transformation from ($V,R$) to FG coordinates ($\tau,z$) takes exactly the same form as in \eq{VRtoFGsolSAdS} (with $Q$ only beginning to affect at $\mathcal{O}(z^7)$ in $V(\tau,z)$ and $\mathcal{O}(z^5)$ in $R(\tau,z)$) and, consequently, that the first few FG metric coefficients are the same as in \eq{FGcoeffsSAdS} (with $Q$ only beginning its influence at $\mathcal{O}(z^6)$ in both $g_{\tau\tau}$ and $g_{ij}$).\footnote{Of course we may want to parametrize the AdSRN metric using not ($M,Q$) but instead ($r_h,Q$), for instance. In this case the FG coefficients are still going to be given by the AdS-Schwarzschild expressions \eq{FGcoeffsSAdS} with $M$ now expressed in terms of ($r_h,Q$) as $M=r_h^4+\frac{Q^2}{r_h^2}$ (and obviously the statement about $Q$ only starting to affect the expansion at higher orders must be forgotten).}
The gauge field appearing in \eq{RNAdSmetricFLRW}, on the other hand, has a nontrivial FG expansion that is readily found to be
\begin{eqnarray}
 A_adx^a &=& \mu\bigg[\frac{1}{a}-\frac{a\ddot{a}-2\dot{a}^2+2r_h^2}{2a^3}z^
 +\cdots\bigg]d\tau -\mu\bigg[\frac{\dot{a}}{a^2}z+\frac{\dot{a}\left(\dot{a}^2-2r_h^2\right)}{2a^4}z^
+\cdots\bigg]dz\ .
\end{eqnarray}

The holographic renormalization for the Einstein-Maxwell system can be found, e.g., in \cite{Sahoo:2010sp}. The expressions for the renormalized stress tensor and $U(1)$ conserved current of the dual CFT are generically given in terms of the FG coefficients as\footnote{Up to scheme dependent terms that do not contribute to the conformal anomaly and can be removed by additional counterterms (see \cite{Sahoo:2010sp} for details).}
\begin{eqnarray}\label{eq:TmunuCFTeinsteinmaxwell}
\bigl\langle T_{\mu\nu}\bigr\rangle &=& \frac{1}{ 4\pi G_5}\left\{g^{(4)}_{\mu\nu}-\frac{1}{2}g^{(2)\sigma}_{\ \mu}g^{(2)}_{\sigma\nu}+\frac{1}{4}\bigl(g^{(2)\sigma}_{\ \sigma}\bigr) g^{(2)}_{\mu\nu}-\frac{1}{8}\bigl[\bigl(g^{(2)\sigma}_{\ \sigma}\bigr)^2g^{(2)}_{\sigma\rho}g^{(2)\rho\sigma}\bigr]g^{(0)}_{\mu\nu}+\frac{1}{48}\bigl(F^{(0)}_{\sigma\rho}F^{(0)\sigma\rho}\bigr)g^{(0)}_{\mu\nu}\right\}\notag\\
\bigl\langle J^{\mu}\bigr\rangle &=& \frac{1}{8\pi G_5}\bigl(A^{(2)}_\nu+B^{(2)}_\nu\bigr)g^{(0)\nu\mu} \ ,
\end{eqnarray}
where $A^{(2)}_\nu$ and $B^{(2)}_\nu$ are the second order coefficients appearing in the FG expansion of the bulk gauge field, i.e.,
$$A_{\nu}(z,x)=A^{(0)}_\nu(x)+z^2\bigl[A^{(2)}_\nu(x)+B^{(2)}_\nu(x)\log z^2\bigr]+\cdots\ .$$
Note that the expression for $\langle T_{\mu\nu}\rangle$ is almost the same as the one for pure Einstein gravity in the bulk, \eq{TmunuCFTeinstein}, the exception being the extra contribution due to the gauge field in the last term. Inserting our FG expansion constructed above gives the following result for the energy density, pressure, and charge density $\mathcal{Q}\equiv\bigl\langle J^{\tau}\bigr\rangle$ of a $U(1)$-charged plasma in a FLRW spacetime
\begin{eqnarray}\label{eq:CFTenergypressureRNAdS}
\mathcal{E} &=& \frac{3\dot{a}^4+12r_h^2(r_h^2+\frac{1}{3}\mu^2)}{64\pi G_5 a^4} \nonumber\\
\mathcal{P} &=& \frac{\dot{a}^4+4r_h^2(r_h^2+\frac{1}{3}\mu^2)-4a\ddot{a}\dot{a}^2}{64\pi G_5 a^4}\nonumber\\
\mathcal{Q} &=& \frac{\mu\bigl(2r_h^2+2\dot{a}^2+a\ddot{a}\bigr)}{16\pi G_5a^3}\ .
\end{eqnarray}
Once again this can be put entirely in 4d CFT language using $G_5=\frac{\pi}{2N_c^2}$, eliminating $r_h$ in favor of the local temperature $T(V)$ as $r_h=\frac{1}{2}\pi aT\bigl(1+\sqrt{1+2\mu^2/3\pi^2T^2}\bigr)$ and, finally, writing $\mu=\tilde{\mu}a$, since the chemical potential associated to the expanding plasma is the time-dependent one $\tilde{\mu}=\frac{\mu}{a}$ instead of $\mu$, as discussed above. The resulting expressions are lengthy and no more instructive than \eq{CFTenergypressureRNAdS}, so we do not show them explicitly here. We just point out, as a sanity check, that for $\mu=0$ the result \eq{CFTenergypressureSAdSin4dlanguagek=0} is sucessfully recovered.

The conformal anomaly in this case is the same as in \eq{CFTanomalySAdS}, i.e., there is no contribution from the chemical potential to the anomaly. The $U(1)$ gauge field usually contributes a term proportional to $\bigl(F^{(0)}_{\mu\nu}\bigr)^2$ (see \cite{Sahoo:2010sp}), but for our solution this is zero since at the boundary we only have $A^{(0)}_\nu dx^\nu=\frac{\mu}{a}d\tau$ (hence $F^{(0)}_{\mu\nu}=0$). It is straightforward to check from \eq{CFTenergypressureRNAdS} that
\begin{eqnarray}
 \nabla_\mu\langle T^{\mu\nu}\rangle &=& 0\notag\\
 \nabla_\mu\langle J^{\mu}\rangle &=& \frac{\mu}{2a^3}\left(-3\dot{a}\ddot{a}+a\dddot{a}\right)\ ,
\end{eqnarray}
i.e., the CFT energy-momentum tensor is conserved while the $U(1)$ current is not. This is a direct consequence of the dynamical chemical potential experienced by the plasma and should not come as a surprise.

\section{Conclusions}\label{sec:AdSFLRWconclusions}

We have introduced a new slicing of AdS black holes such that a non-standard notion of conformal boundary with a FLRW metric can be defined.
The construction is based on the use of Eddington-Finkelstein coordinates instead of early approaches involving Fefferman-Graham coordinates, a fact that makes the task tremendously simpler and applicable to a large class of AdS black holes including eventual supporting matter fields. It also provides a good perspective into the numerical study of expanding plasmas in holography using the characteristic formulation of the Einstein equations in AdS \cite{Chesler:2013lia}, for which the use of EF coordinates is determinant. A Fefferman-Graham expansion near the new \lq\lq cosmological\rq\rq~boundary can be easily constructed to any desired order for the FLRW-foliated metric, which leads to the renormalized stress tensor of the dual expanding CFT plasma upon the assumption that the standard holographic renormalization procedure is still applicable. In particular, the results of \cite{Apostolopoulos:2008ru} are consistently recovered as a simple application to the AdS-Schwarzschild solution and then generalized to include a second central charge (using the AdS-Gauss-Bonnet black hole) or a nonvanishing chemical potential (using the AdS-Reissner-Nordström solution) for the dual CFT plasma.

The new dynamical foliation elucidates the procedure carried out in \cite{Buchel:2016cbj} by clarifying the assumptions involved and the background solution on which the perturbative study of the expanding $\mathcal{N}=2^*$ plasma close to conformality relies. It also provides, as a by-product of the application to the AdS-Reissner-Nordström solution, the interesting lesson that the nonequilibrium dynamics of a CFT plasma subject to a quench $\tilde{\mu}(t)$ in the chemical potential resembles a cosmological evolution with the scale factor $a(t)$ being inversely related to the quench profile, $a(t)\sim \tilde{\mu}(t)^{-1}$. A similar conclusion can be drawn for a wider class of quenches of CFTs by applying our slicing to the corresponding dual static hairy black hole solution, since the (time-independent) non-normalizable mode associated with static matter field configurations naturally acquires time dependence in the new ($V,R$) coordinates.

The proposal also gives a novel tool to analytically explore properties of expanding plasmas that have not yet been explored. This involves, for instance, a study of the time evolution of nonlocal observables with a known holographic dual gravity description, such as higher-point correlators, Wilson loops and the entanglement entropy of spatial subsystems. However, we choose to postpone this to a subsequent work.

\subsection*{Acknowledgements}
I am very grateful to Elcio Abdalla, Jorge Noronha, Ricardo Landim, Viktor Jahnke and Leonardo Werneck for useful comments and discussions. I also thank Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for financial support.

\bibliographystyle{JHEP}

redpajama_set_name: RedPajamaArXiv


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text:
1982 год в истории Канады.

События без точной даты
В 1982 году экономика Канады испытывала острый и затяжной кризис. Число банкротств увеличилось почти на треть, число безработных достигло полутора миллионов человек.

События с датами

Февраль
Первые сообщения о случаях СПИДа в Канаде.

14 февраля — 84 человека погибли в результате опрокидывания нефтяной платформы Ocean Ranger.

Март
На 11 Международном фестивале короткометражных фильмов в Лилле в категории художественных фильмов главный приз поделили фильмы «Элвис Греттон» (режиссёры П.Фалардо и Ж.Пулен (Канада)) и «Лавка со сладостями» (режиссёр К.Кервен (США)).

8 марта — Акт о Канаде получил одобрение Палаты общин Великобритании.

Апрель
17 апреля — Королева Великобритании Елизавета II подписала Акт о Канаде и новая конституция Канады вступила в силу. В отличие от действовавшего до этого момента Конституционного акта 1867 года в новой конституции добавлена глава о правах и свободах канадских граждан и о гарантиях этих свобод в масштабах федерации. Поправки к канадской конституции более не подлежат утверждению британским парламентом.

28 апреля — на выборах в Саскачеване побеждает Грант Девайн из Прогрессивно-консервативной партии, опередивший Аллана Блейкни (НДП).

Май
На 7 Международном музыкальном фестивале в Тулоне вторая премия присуждена Р.Дж. Ранти (Канада).

8 мая — на Гран-при Бельгии погиб известный канадский автогонщик, пилот команды «Феррари» Жиль Вильнёв.

8 мая — Грант Девайн становится премьер-министром Саскачевана.

23 мая — Андре Бессетт причислен к лику блаженных римским папой Иоанном Павлом II.

Июнь
На 5 Всемирном фестивале мультипликационного кино в Загребе премии удостоены фильмы «Э» (режиссёр Б. Пояр), «Птица-поросёнок» (режиссёр Р. Конди), премия за дебют присуждена фильму «Луна, луна, луна» (режиссёр В. Эльнекав).

13 июня в Монреале состоялся Гран-при Канады. Победителем стал Нельсон Пике. На старте гонки погиб молодой гонщик Риккардо Палетти.

Июль
На 23 Международном кинофестивале в Карловых Варах премии за лучшее исполнение мужской роли удостоены Генри Фонда («На золотом озере», режиссёр Марк Райделл, США) и Дональд Сазерленд («Перешагнуть порог», режиссёр В. Пирс, Канада).

 24 июля — родился Лука Маньотта — актёр гей-порно.
 26 июля — Карэн Болдуин становится победительницей конкурса Мисс Вселенная в Лиме, Перу. Первая канадка, выигравшая этот конкурс.

Август
23 августа — в Оттаве армянскими террористами из организации Бойцы за справедливость в отношении геноцида армян убит турецкий военный атташе Атилла Алтикат.

Сентябрь

В Торонто завершено строительство здания «Рой-Томсон-холл» (проект фирмы «Артур Эриксон ассошиэйтс», архитекторы Матерс и Холденби). В новом здании начал работать Торонтский симфонический оркестр (дирижёр Э. Дейвис) и хор имени Мендельсона (дирижёр Э. Айзелер).

Октябрь
27 октября — День Доминиона переименован в День Канады.

Ноябрь
Премьер-министр Канады Пьер Эллиот Трюдо посетил СССР (принял участие в похоронах Леонида Ильича Брежнева), состоялась беседа Николая Александровича Тихонова с Пьером Эллиотом Трюдо.

2 ноября — на выборах в Алберте вновь побеждает Питер Локхид из прогрессивно-консервативной партии.

Декабрь

10 декабря — официально признана Канадская экономическая зона шириной в 200 морских миль (370 км).

Спортивные достижения Канады в 1982 году

Чемпионат мира по горнолыжному спорту (28 января — 7 февраля), Шладминг (Австрия).

Скоростной спуск (женщины): Д.Сёренсен — золотая медаль, Л.Грэхэм — бронзовая медаль.

Чемпионат мира по скоростному бегу на коньках (6 — 7 февраля), Алкмар (Нидерланды).

Спринтерское многоборье (мужчины): Гаэтан Буше — серебряная медаль.

Чемпионат мира по фигурному катанию (9 — 13 марта), Копенгаген (Дания).

Одиночное катание (мужчины): Брайан Покар — бронзовая бедаль.

Чемпионат мира и Европы по хоккею (15 — 29 апреля), Тампере, Хельсинки (Финляндия)

Сборная Канады — бронзовая медаль.

Чемпионат мира по гребле на байдарках и каноэ (28 июля — 1 августа), Белград (СФРЮ).

Байдарка-двойка (1000 метров) — серебряная медаль.

Чемпионат мира по плаванию, прыжкам в воду, водному поло и синхронному плаванию (29 июля — 7 августа), Гуаякиль, (Эквадор).

Женщины.

Брасс, 100 м: Э.Оттенбрайт — серебряная медаль (вместе с К.Роденбах (США)).

Брасс, 200 м: Э.Оттенбрайт — бронзовая медаль.

Мужчины.

Брасс, 100 м: Виктор Дэвис — серебряная медаль.

Брасс, 200 м: Виктор Дэвис — золотая медаль.

Синхронное плавание.

Одиночное плавание: К.Кришка — серебряная медаль.

Парное плавание: Канада (С.Хэмбрук и К.Кришка) — золотая медаль.

Групповое плавание: Канада — золотая медаль.

Чемпионат мира по вольной борьбе (11 — 14 августа), Эдмонтон (Канада).

2 средний вес: К.Дэвис — серебряная медаль.

Чемпионат мира по академической гребле (22 — 29 августа), Люцерн (Швейцария).

Женщины.

Двойка парная: Канада — бронзовая медаль.

Двойка распашная: Канада — бронзовая медаль.

Чемпионат мира по стрелковому спорту (2 — 14 ноября), Каракас (Венесуэла).

Траншейный стенд:

С.Нетресс — серебряная медаль.

Персоналии

Верховная власть
 Глава государства (монарх) — королева Елизавета II (консорт — принц Филипп, герцог Эдинбургский)

Федеральное правительство
 Генерал-губернатор — Эдвард Шреер
 Премьер-министр — Пьер Эллиот Трюдо

Премьер-министры
 Премьер-министр Альберты — Питер Локхид
 Премьер-министр Британской Колумбии — Билл Беннетт
 Премьер-министр Манитобы — Ховард Паули
 Премьер-министр Нью-Брансуика — Ричард Хатфилд
 Премьер-министр Ньюфаундленда и Лабрадора — Брайан Пекфорд
 Премьер-министр Новой Шотландии — Джон Бучанан
 Премьер-министр Онтарио — Билл Дэвис
 Премьер-министр Острова Принца Эдварда — Джеймс Ли
 Премьер-министр Квебека — Рене Левек
 Премьер-министр Саскачевана — Грант Девайн

Родились

 10 марта — Кэтлин Студи, пловчиха
 18 марта — Мэтью Ломбарди, хоккеист
 30 марта — A-Trak, диджей и музыкант
 14 апреля — Лиз Левейль, гимнастка
 16 апреля — Арон Фелтхам, ватерполист
 12 мая — Райан Уилкинсон, футболистка
 16 июня — Кэти Тремблей, триатлонистка
 23 июня — Дерек Бугард, хоккеист
 6 июля — Келли Стефанишин, пловчиха
 1 сентября — Джеффри Баттл, фигурист, бронзовый призёр ХХ олимпийских игр в Турине в 2006 году, чемпион мира 2008 года
 3 сентября — Сара Бёрк, фристайлистка
 29 ноября — Элизабет Коллинз, пловчиха
 13 декабря — Дэн Хэмьюс, хоккеист
 30 декабря — Кристин Кройк, актриса

Умерли

 28 марта — Уильям Фрэнсис Джиок, химик и лауреат Нобелевской премии (р.1895)
 8 мая — Жиль Вильнёв, автогонщик, пилот Формулы-1 (р.1950)
 28 июня — Игорь Гузенко, русский перебежчик (р.1919)
 25 июля — Хэл Фостер, карикатурист (р.1892)
 4 октября — Гленн Гульд, пианист (р.1932)
 16 октября — Хью Джон Флемминг, политик и 24-й премьер-министр Нью-Брансуика (р.1899)
 16 октября — Ганс Селье, эндокринолог (р.1907)
 18 октября — Джон Робартс, адвокат, политик и 17-й премьер-министр Онтарио (р.1917)
 2 ноября — Д. Дьюи Сопер, арктический исследователь, зоолог, орнитолог и писатель (р.1893)
 19 ноября — Ирвинг Гофман, социолог и писатель (р.1922)
 29 ноября — Перси Уильямс, легкоатлет, двукратный олимпийский чемпион (р.1908)
 7 декабря — Гарри Джером, легкоатлет (р.1940)
 19 декабря — Джордж Исаак Смит, адвокат, политик и премьер-министр Новой Шотландии (р.1909)

Примечания

redpajama_set_name: RedPajamaWikipedia


text:
Looking for Color, Promoting the Untold Story of a Free Family in Salisbury and Sharon, Connecticut.
Students from Salisbury School's Searching for Slavery class, in conjunction with the Upper Housatonic Heritage Area, are excited to screen the premiere of their film, Looking for Color on May 26, 2021, at 7:00 p.m. for Noble Horizons. Among several class projects, this film is one of three documentaries students have created over the course of the year to carry out their mission of educating the public about this important history, rewriting the stories that have been recorded incorrectly, and uncovering lives that have been ignored or buried.
This work builds on the successful unveiling of a Witness Stone for Norfolk, Connecticut's own formerly enslaved author, abolitionist, and civil rights hero, James Mars on May 1, 2021. The day featured speeches from Connecticut's first Black Congresswoman, Jahana Hayes as well as a Proclamation signed by Governor Ned Lamont.
"This movie has forced us to confront history that challenges our perception of who we are and how we became a country. Looking at the contributions local families of color like the Mars and the Cesars have had on our communities has really opened our eyes," says Looking for Color's Producer Nicholas Gray. "In turn, our aim is to use our work to help form a more complete and inclusive history that highlights the contributions of all Americans. This project is not about simply uncovering the history of one Black Family in America, it is also about completing the inaccurate and incomplete history of our diverse American Family. We are excited to once again share this work with our friends at Noble Horizons."
Throughout our 2020-2021 school year, students at the Salisbury School have been searching for color in the history of the northwest corner of Connecticut and the Berkshires. They have used state and town records, consulted local historians and authors, and visited local sites that has allowed them to, quite literally, search for the buried or ignored Black history of the Upper Housatonic River Valley.
To sign up, click here
See more at @findingslavery on Instagram and @slaverynorth on Twitter.
By MainStreetMag|2021-05-24T11:27:06-04:00May 24th, 2021|Main Street|


Pick up some top SEO tips to help improve your photography business.
SEO shouldn't be scary, or confusing.
The only reason it seems that way is that SEO nerds (like me) often write articles for other SEO nerds which means we use a bunch of technical jargon to explain things to one another.
This is just like a veteran photographer giving their niece her first camera and instead of explaining it to her in terms she'd understand (as a newbie), he explains it to her over-using phrases like ISO, Aperture & F-Stop, shutter speed, etc.
A newbie doesn't need all of that. In fact, it makes it sound so foreign that she may not even enjoy using the camera. SEO is the same way. I know based on my extensive work helping photographers grow a pipeline of leads on autopilot using SEO.
This article is going to demystify SEO and give you five tips that you can implement in your business and see real returns.
Why Does SEO Matter for Photographers?
Google is both a discovery platform and a research platform. If I'm searching for an answer to a problem I have, I Google it. If I know what I want to find, but want to learn more, I Google it.
According to an Advanced Web Ranking study (and confirmed by many more), 42% of people click on one of the first 3 search results in Google.
In hard numbers, that means that if you rank first for the searches related to "real estate photography in Cleveland," and 200 people search for that each month, 54 people (27%) are going to click over to your website. IF your site is awesome and converts traffic to leads, you could be getting 5-10 solid leads coming in per month on autopilot.
Every time I hire somebody, I Google them first. Even if a friend has recommended them, I Google them.
And you know what? I'm not alone. 97% of consumers check online before hiring you. Even if you're already 99% of the way to closing a new client, they're still going to Google you.
Important: SEO isn't dangerous, but if you go nuts with it trying to game the system, it can backfire. The advice in this article is evergreen (it will work forever). These are scammy hacks to game the rankings. One of my clients was having somebody build spammy links for $125 per month and as soon as I saw it, we put in a plan to fix it and her traffic shot up like a rocket.
Never forget that the goal of SEO is to bring in traffic from search engines (mainly Google) to your website. This traffic only matters if that traffic becomes leads and those leads become clients. Otherwise, it's just a vanity metric like that Facebook page with 26,946 followers that never brings in a high-value client.
Side Note: This is not a "skim" article. You *can* skim it and learn what you should do, but all I care about is increasing the revenue in your business. You can't do that skimming articles.
Read this entire article (it's not that long, I promise) and ask me any questions you have in the comments below. I read every single one.
You might think that you know your ideal client pretty well, but do you know them well enough to get inside their head and predict what they're searching for in Google?
Instead of writing what we "guess" they'd be searching for, you can find out and start to increase your traffic and leads.
*Note: For examples like this, I like to use free tools versus paid tools because it makes it much easier for you, the reader. When I do this for clients, I use paid tools to increase the speed and quality of my service.
Again, I recommend Google Adwords because it's free and since you're a photographer (and not an SEO expert), there's no reason for you to pay tonnes of money each month for SEO tools.
3. Get Ready for Ideas!
Click the "Keyword Ideas" tab and download them in Excel format.
From here, I like to delete all of the columns except "Keyword" (B) and Competition (E).
Now, by scrolling down the "keyword" column, you'll get a myriad of ideas.
Pro Tip: Filter the "keyword" column by right clicking the top and narrowing it down to only searches that include your keywords or maybe one of your keywords. Like me, I doubt you have time to go through 600 keyword ideas, so filter them to get the most relevant ones.
What's super cool about figuring out this process is that, since we can see what people Google for, it's pretty much the same as interviewing your potential clients.
This is probably the most confusing things. Most SEO for photographer articles just tell you to make great content and they don't ever explain how.
So let me break it down: There are too many conflicting pieces of advice out there about what kind of content to make. Some say make short content more often and others say to write long definitive guides. What ends up happening is that you, the photographer, get a case of what I call "analysis paralysis" and you don't take any action or publish anything at all. So look at what I do and what all successful SEOs do: We write authoritative content that is genuinely helpful to people.
Every article I write takes over 5 hours from start to finish. Most, like this one, take over 20 hours. I love my family a lot more than I love writing about business and I'd rather be playing lightsabers with my sons or doing pull-ups in my backyard, but I know what it takes to rank, so I do it. I don't make content not worth making, and neither should you.
I research keywords (just like I told you how to do above).
Continuing with the example above, I think that the real estate photographer should definitely write articles about the incredible homes that she has photographed, but she also needs to write articles that get shared in social and get linked to. What if she found the five most expensive homes in her city and took photos of those and make it into an article titled "Behind The Curtain of the Five Most Expensive Homes in Cleveland." Or, maybe just one article on the most expensive home in Cleveland. I bet that would get the attention of Google and the real estate agents that want to hire her.
These will build trust in the real estate agents who are going to pay you $10,000+ to photograph their listings over the next year, so don't look cheap in your writing.
Title - Use your main keywords and the location. Lots of photographers use the names' of people in the session, but since those aren't going to pull in any significant traffic, there's no reason. With Keyword + Location, Google knows what kind of session you did (such as Aberdeen Manor Wedding in Valparaiso, Indiana).
Content - This is where you talk about your subject. Explain your relationship with them and tell a story about something that didn't go according to plan (doesn't that always happen?). Elaborate on how you overcame the potential derailment. In the mind of your potential client, this positions you in their mind as "the expert" who they can trust with a photo session.
A link to get in touch - I'm a big fan of a link to your contact page, but I've also seen a few photographers have success with a phone number link (auto-dials in on mobile devices) or a link to join a mailing list.
5 images from the session - Why only five images? If a potential client can't decide to hire you after seeing five images, fifty images aren't going to sell them.
Another link to get in touch (yes, I'm serious) - Don't make them scroll back up after they see your images. The fewer steps a client has to take before hiring you, the better.
Since photography has a high demand of people searching online and a large cost of service, competition is going to be fierce.
SEO for wedding photographers won't be as competitive as the plastic surgery industry (SUPER high demand AND cost), but will definitely be more competitive than local art gallery SEO.
I've looked at over 500 photographer's websites, links, tags, etc. and just by reading this guide and implementing it, you're going to be in the top 1%.
BUT, if you have somebody in your niche that's also in that 1%, you need to know what they're doing and how they're doing it. Don't worry, they're doing it to you, too!
I'm a huge fan of using Moz and Majestic plugins in the Chrome browser. Install them and do a quick signup and you're ready to go.
If you prefer to use one over the other, no problem. But it's like using only one of the tigers of Voltron, you don't get the full effect.
Domain Authority (DA) - How many other websites are linking to the site's main domain (like Mistilayne.com). This is the Domain Authority (DA).
Look at the number of backlinks each one has. Having more than your competition is the difference between a six-figure photographer and one that's about to quit from lack of work. Typically, the best links for a photographer are from other photography sites and other local sites. Look at ones your competition has and reach out to those sites to get them, too!
Is this a lot of work? Of course. Is it worth it? Absolutely! But, it's also the reason a lot of people hire professionals to do it for them.
This used to be the easiest part of the process, but things have changed since I started on the web in 2010.
Share links on social media, on forums, Reddit, Quora, etc.
While buying ads on Wedding Wire, The Knot, etc. can be helpful for traffic and SEO, a better option is looking at local blogs in your area. If you're a photographer in Philadelphia, a link from Billy Penn would be amazing. Wedding photographer in Chicago? Get a sponsored link from the Chicago Sun Times would be extremely valuable, and cheap considering the added benefit of traffic and Google rank in bringing in new clients.
I saved this for last because guest posting is my favourite. You get to provide value to somebody's readers and you get a link (and maybe some traffic) in return.
Sending them an email with sample headlines based on posts they have that already do well (find these by dropping their site URL into Buzzsumo), is the best way to get on their radar.
In the most simple terms, everything within your site should point toward your contact and services page. Every blog post, about page, etc.
Everything. We want to drive as much traffic as possible to a place where leads can become customers. If you're super savvy and are building a mailing list (the #2 thing I see photographers neglect behind SEO), directing them to join that list via some sort of lead magnet (a wedding day checklist or portrait outfit guide are perfect) is also a great idea.
Back in 2010, this meant posting to your fan page and personal profile, but in 2017, this means writing things for your ideal clients, and also your peers.
Re-read that last line and don't forget it. You want other photographers sharing your posts AND your potential clients so alternating between topics is super important.
Since you already know you should be on social media: Facebook, Pinterest, and Instagram (Twitter is pretty optional now), I'll share my two gold mines for traffic and links: Quora and Reddit. Search for your keywords on each and leave helpful replies with links to your site at the end. I've pulled a ton of traffic to clients' websites from Quora posts like "Who is the best photographer is San Francisco?" and questions like that.
Building an honest relationship and making it a win for both the site owner and you is key here. They get amazing content that helps their goals (traffic, subscribers, etc.) and you get things that will help you rank in Google.
Every single photography Facebook group, LinkedIn group, and forum is plagued with posts about photographers lamenting all of the newbies jumping in and stealing their business.
It makes me think that we've forgotten that this *is* a business we're running. None of us are promised clients just because we do good work. We have to learn to be great at business as well.
SEO is hard, but only as hard as it has to be to keep crappy photographers and "dabblers" from putting in the work.
But you're a pro and if you're willing to implement everything that I've written above, clients are going to be beating down your door. Some photographers have even made an extra five-figures this year using these tactics. The best part of SEO is that we can track that, and prove it in their analytics!
SEO is the most important investment you can make in your business. Good thing you have an expert here to help. I read every single comment (I promise!) so if you have a question about ANYTHING, just comment below and I'll reply!
Brendan Hufford is a marketing and business veteran who is absolutely in love with photography. In 2016, he founded Photo MBA, where he teaches photographers how to charge more, land better clients, eliminate business headaches, and bridge the gap between their current reality and photography business goals.
If have no idea what SEO is so perhaps tip ﹟0 should have given a definition ?
"The only reason it seems that way is that SEO nerds (like me) often write articles for other SEO nerds which means we use a bunch of technical jargon to explain things to one another"
So technical that there was no explaination to a newbie what SEO stood for; LOL, I had to Google it!!
Great article, bound to help me when I get off my bum and build that website I keep saying I will.
Bookmarked the article to come back to later.


Then, merge these two and find the required final states.
Initial state of these DFA will be the state which contains the initial states of those two separate machines. As, q0 and q2 are the initial states thus, q0q2 is the initial state of the final DFA.
This machine accept that languages which contains either odd no. of 0's or even no. of 1's. As we know that q1 indicates odd no. of 0's and q2 indicates even no. of 1's. So, the final states of the required DFA will contain either q1 or q2.
This is our required DFA which accept the languages containing odd no. of 0's or even no. of 1's.
This machine accept that languages which contains odd no. of 0's and even no. of 1's. As we know that q1 indicates odd no. of 0's and q2 indicates even no. of 1's. So, the final states of the required DFA will contain both q1 and q2.
This is our required DFA which accept the languages containing odd no. and 0's or even no. of 1's.
This machine accept that languages which contains either odd no. of 0's or even no. of 1's but not that languages which contains both odd no. of 0's and even no. of 1's. As we know that q1 indicates odd no. of 0's and q2 indicates even no. of 1's. So, the final states of the required DFA will contain exactly one among q1 and q2.
This is our required DFA which accept the languages containing odd no. of 0's or even no. of 1's but not the both together.


Celestron NexStar 6 SE Telescope. Condition is New. Shipped with USPS Parcel Select Ground.
Box unopened, telescope in perfect condition and unused. Got it as a gift and don't plan to use it. I can open the box and show you more pictures if you request it.


Come join us during Christmas break for a Jr. Guard bootcamp. Learn about what it takes to be a lifeguard, such as recognizing a drowning victim, how to assist someone who is struggling in the water and how to perform CPR and first aid. You must be able to swim 25 yards front crawl and 25 yards breaststroke as well as tread water for one minute and float for 30 seconds on your back. Upon completion each student will receive an American Red Cross CPR and First Aid Certification.